2. One of the important factors in auto safety is the weight of the vehicle. Ins

Question

2. One of the important factors in auto safety is the weight of the vehicle. Insurance companies are interested in knowing the mean weight of cars currently licensed in the United States; they believe it is 3000 pounds. To see if that assumption is correct, they checked a random sample of 101 cars. For that group the mean weight was 2867 pounds, with a standard deviation of 541.8 pounds. Perform a test at ? = 0.01 to determine if the true mean weight of all cars is different than 3000 pounds. State your hypotheses, find the test statistic and critical value, and state your conclusion.

Explanation / Answer

Null hypothesis Ho:mu=3000

Alternative hypothesis mu=/=3000

n=101

Xbar=2867

sd = 541.8

Since we have sample sd known we have to use t test

t= (Xbar-mu)/(sd/sqrt(n))

so., t= (2867-3000)/(541.8/sqrt(101)) = -2.467024

while the critical values of t at 0.01 sigificance from t tabe at 100 degrees of freedom (i.e. n-1 degrees of freedom)

is -2.625891 to +2.625891

and the calculated t value -2.467024 falls in the above range and hence we conclude that we can't reject Ho.

So we conclude that mean weight is 300 pounds

Hope the above ans has helped you in understanding the problem. Pls upvote if it has really helped you. Good Luck!!

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